Geometry Locus and Constructions
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What is the locus of points from a point?
A circle that has the point as a center.
What is the locus of points that are equidistant from two points?
A line that is the perpindicular bisector to the segment that connects them.
What is the locus of points that is quidistant from a line?
Two lines that are parallel to the line and or on opposite sides of the line.
What is the locus of points equidistant from two lines?
A line between the two lines that is parallel and the same distance away on both sides.
What is the locus of points that are equidistant from two intersecting lines?
A line that is the angle bisector.
How do you copy a line segment?
Place the point of the compass on point the endpoint. Stretch the compass so that the pencil is exactly on the other endpoint. Without changing the spot you pencil is in on the compass, place the compass point on the starting point on the reference line and swing the pencil so that it crosses the reference line.
How do you copy an angle?
Place the point of the compass on the vertex. Stretch the compass to any length that intersects the angle. Swing an arc with the pencil that crosses both sides of the angle. Without changing the spot your pencil is in on the compass, place the compass point on the starting point of the reference line and swing an arc that will intersect the reference line and go above the reference line. Go back to the orignal angle and measure the width of the arc from where it crosses one side of the angle to where it crosses the other side of the angle. With this width, place the compass point on the reference line where your new arc crosses the reference line and mark off this width on your new arc. Connect this new intersection point to the starting point on the reference line, and you have copied the angle.
How do you bisect a line segment?
Place your compass point one endpoint and stretch the compass MORE THAN half way to the other endpoint, but not beyond it. With this length, swing a large arc that will go BOTH above and below the line. Without changing the spot your pencil is in on the compass, place the compass point on the other endpoint and swing the arc again. Connect the two points of intersection. This new straight line is now the perpindicular bisector of the segment.
How do you bisect an angle?
Place the point of the compass on the vertex. Stretch the compass to any length as long as it intersects the angle. Swing an arc so the pencil crosses both sides of the angle. This will create two intersection points with the sides of the angle. Place the compass point on one of these new intersection points on the sides of the angle. If needed, stretch your compass to a sufficient length to place your pencil well into the interior of the angle. Stay between the sides of the angle. Place an arc in this interior - you do not need to cross the sides of the angle. Without changing the width of the compass, place the point of the compass on the other intersection point on the side of the angle and make the same arc. Your two small arcs in the interior of the angle should be crossing. Connect the point where the two small arcs cross to the vertex the of the angle.
How do you make a parallel line that passes through a point?
With your straightedge, draw a transversal through the point. Using your knowledge of the construction COPY AN ANGLE, construct a copy of the angle formed by the transversal. The vertex of your copied angle will be the point When the copy of the angle is complete, you will have two parallel lines when you strech the lines through.
How do you make a perpindicular line from a point?
Place your compass point on the point and sweep an arc of any size that crosses the line twice. Place the compass point where the arc crossed the line on one side and make an arc ON THE OPPOSITE SIDE OF THE LINE. Without changing the spot your pencil is in on the compass, place the compass point where the arc crossed the line on the OTHER side and make another arc. Your two new arcs should be crossing on the opposite side of the line. With your straightedge, connect the intersection of the two new arcs to point P.
How do you make a triangle with specified lengths?
With the lengths given, take your end point, and swoop it around to make the point. From each point, swing a different length. Connect the points of intersection to get the desired triangle.
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